We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are the complexity of the loss-landscape and of the dynamics within it, and to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes are different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized.

本研究利用玻璃系统在统计物理学上所开发的方法对深度神经网络(DNN)的训练动态进行了数值分析，在地址复杂度的损失面貌和网络结构等方面取得了一些独到的发现。

比较动态：深度神经网络与玻璃系统